Question 1

Which of the following is the correct formula for the average rate of change of a function $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 2

Given $$f(x) = x^2$ - 4x + 3$$, what is the average rate of change from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$-3$$

Question 3

Which transformation will reflect the graph of $$f(x)$$ over the $$y-$$axis?

Accepted Answer

$$f(-x)$$

Question 4

If $$g(x) = f(x) + 2$$, how is the graph of $$f(x)$$ transformed to obtain $$g(x)$$?

Accepted Answer

Shifted up by 2 units

Question 5

Given $$f(x) = |x|$$, which graph represents $$f(x-2)$$?

Accepted Answer

The graph of $$|x|$$ shifted right by 2 units

Question 6

Which of the following is the correct formula for the difference quotient of $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 7

If $$f(x) = x^2$, what is the value of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 8

Which transformation will shift the graph of $$f(x)$$ down by 3 units?

Accepted Answer

$$f(x) - 3$$

Question 9

Given $$f(x) = x^2$ and g(x) = f(x-1) + 2$, which sequence of transformations is applied to f(x$$)$$ to obtain g(x$$)$$?

Accepted Answer

Shift right by 1 unit, then up by 2 units

Question 10

If $$f(x) = x^2$ and h(x) = -f(x$$)$$, what is the effect on the graph?

Accepted Answer

Reflection over the $$x-$$axis

Question 11

Which of the following represents a vertical stretch of $$f(x) by a $$factor of 3?

Accepted Answer

$$3f(x)$$

Question 12

Given $$f(x) = x^2$, what is the equation for the graph reflected over the y$-axis and shifted up by 4 units?

Accepted Answer

$$f(-x) + 4$$

Question 13

If $$f(x) = x^2$ and g(x) = f(-x) - 2$, what is the transformation from f(x$$)$$ to g(x$$)$$?

Accepted Answer

Reflect over $$y-$$axis, then shift down by 2 units

Question 14

Which of the following is the correct formula for the composition $$(f \circ g)(x)$$?

Accepted Answer

$$f(g(x))$$

Question 15

Given $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 16

If $$f(x) = x^2$ and g(x) = x + 1$, what is (g$$ \circ f)(2)$$?

Accepted Answer

$$5$$

Question 17

Which of the following describes the transformation $$f(x) 	o f(x+3)$$?

Accepted Answer

Shift left by 3 units

Question 18

Given the piecewise function $$h(x) = \begin{cases} 2x+1 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, what is $$h(-2)$$?

Accepted Answer

$$-3$$

Question 19

Which of the following is the correct formula for the sum of two functions $$f$$ and $$g$$?

Accepted Answer

$$(f+g)(x) = f(x) + g(x)$$

Study Guide: Graphs and Transformations of Functions in Precalculus

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